Polymers are very long chains formed by the combination of small molecules (monomers) - and have many varying uses in modern daily life. There are three main types of polymer that you need to be aware of - polyalkenes, polyesters and polyamides - and two main types of polymerisation reaction as described below:
This is the simplest mechanism - whereby unsaturated monomers (i.e. alkenes) combine to form a much larger saturated polymer. The most famous examples of this process would probably be the production of poly(styrene) from phenylethene and poly(ethene) from ethene. Note that in each case it is the double bond that splits and bonds to the next molecule in the chain - so poly(stryene) has a central alkyl chain with phenyl side groups attached to it.
Addition polymers are non-biodegradable, and can produce toxic products in disposal - especially by burning, such as in the case of poly(chloroethene) [which is also referred to as "poly(vinylchloride)" or pvc]. However, they generally have very useful properties and so are ubiquitous despite their environmental impact.
This mechanism is so called because a small molecule such as water or hydrochloric acid is released with each addition to the chain.
For polyesters, the usual esterification mechanism is used - between acid and alcohol groups - but with each monomer molecule having a pair of the groups. Most often, a combination of dicarboxylic acids and diols is used, but sometimes monomers can be hydroxy dicarboxylic acids (i.e. with one of each group). Each end of the molecule bonds to one other - and so a chain is formed.
For polyamides, much the same mechanism occurs, but with a peptide link between monomers (i.e. CONH) with a nitrogen atom in place of the oxygen present in polyesters. The reactant groups are amines and carboxylic acids - and synthetic polyamides are mostly created from dicarboxylic acids and diamines a similar way to polyesters. However, you also need to be aware of natural polyamides - in biological systems, amino acids combine via peptide links to produce proteins. The only difference is that in nature amino acids are used whereas artificially dicarboxylic acids are combined with diamines.
Because of their ester or peptide bonding, condenstation polymers are polar - therefore they often have very high melting points and can be extremely strong, depending on the regularity of their structure. Kevlar®, for example, is a polymer made from benzene-1,4-dicarboxylic acid and benzene-1,4-diamine (1,4-diaminobenzene).
Condensation polymers can be broken down by hydrolysis to recover the original monomers - which means that they are biodegradable and so easier than addition polymers to dispose of, but also are inappropriate for some uses involving long term regular exposure to water.